Hyperbolic "Smoothing" of Shapes

We have been developing a theory of generic 2-D shape based on a reaction-diffusion model from mathematical physics. The description of a shape is derived from the singularities of a curve evolution process driven by the reaction (hgperbolic) term. The diffusion (parabolic) term is related to smoothing and shape simplification. However, the unification of the two is problematic, because the slightest amount of diffusion dominates and prevents the formation of generic first-order shocks. The technical issue is whether it is possible to smooth a shape, in any sense, without destroying the shocks. We now repod a constructive solution to this problem, by embedding the smoothing term in a global metric against which a purely hyperbolic evolution is performed from the initid curve. This is a new flow for shape, that extends the advantages of the original one. Specific metrics a m developed, which lead to a natural hierarchy of shape features, analogous to the simplification one might percei...

• Type: Conference
• Year: 1998
• Where: ICCV
• Authors: Kaleem Siddiqi, Allen Tannenbaum, Steven W. Zucker
• Keywords: Computer Vision, Generic 2-D Shape, Generic First-order Shocks, ICCV 1998, Shape Simplification